{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>problem</th>\n",
       "      <th>reasoning</th>\n",
       "      <th>deepseek_solution</th>\n",
       "      <th>ground_truth_solution</th>\n",
       "      <th>correct</th>\n",
       "      <th>judge_reasoning</th>\n",
       "      <th>extracted_answer</th>\n",
       "      <th>extracted_gold</th>\n",
       "      <th>verifier_label</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Let \\( a, b, c \\) be positive real numbers. Pr...</td>\n",
       "      <td>Okay, so I need to prove this inequality: \\(\\f...</td>\n",
       "      <td>To prove the inequality \\n\\n\\[\\n\\frac{1}{a(1+b...</td>\n",
       "      <td>1. Consider the given inequality:\\n\\n\\[\\n\\frac...</td>\n",
       "      <td>True</td>\n",
       "      <td>The provided solution correctly demonstrates t...</td>\n",
       "      <td>['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...</td>\n",
       "      <td>['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A set consists of five different odd positive ...</td>\n",
       "      <td>Okay, so I need to figure out how many differe...</td>\n",
       "      <td>To determine the number of different sets of f...</td>\n",
       "      <td>\\n1. **Observe the Structure of \\( N \\)**:\\n  ...</td>\n",
       "      <td>False</td>\n",
       "      <td>The provided solution computes a total of 25 s...</td>\n",
       "      <td>['25', '25']</td>\n",
       "      <td>['24', '24']</td>\n",
       "      <td>False</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Given real numbers \\( a, b, c \\) and a positiv...</td>\n",
       "      <td>Okay, let's try to tackle this problem step by...</td>\n",
       "      <td>Given real numbers \\(a, b, c\\) and a positive ...</td>\n",
       "      <td>\\nWe begin by analyzing the function \\( f(x) =...</td>\n",
       "      <td>True</td>\n",
       "      <td>Both the provided solution and the ground trut...</td>\n",
       "      <td>['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']</td>\n",
       "      <td>['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>In triangle $ABC$, $CA = CB$, and $D$ is the m...</td>\n",
       "      <td>Okay, so I have this geometry problem here. Le...</td>\n",
       "      <td>In triangle \\(ABC\\), \\(CA = CB\\), making it is...</td>\n",
       "      <td>1. **Identify Key Elements**: Consider \\( \\tri...</td>\n",
       "      <td>True</td>\n",
       "      <td>The provided solution correctly follows the lo...</td>\n",
       "      <td>['D', 'DE \\\\cdot DF = DA^2']</td>\n",
       "      <td>['D', 'DE \\\\cdot DF = DA^2']</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r...</td>\n",
       "      <td>Okay, so I need to figure out which of the giv...</td>\n",
       "      <td>To determine which of the given statements is ...</td>\n",
       "      <td>Given the values:\\n\\[ p = 2^{3009}, \\quad q = ...</td>\n",
       "      <td>True</td>\n",
       "      <td>The solution provided correctly follows the st...</td>\n",
       "      <td>['D', 'D']</td>\n",
       "      <td>['D', 'D']</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                             problem  \\\n",
       "0  Let \\( a, b, c \\) be positive real numbers. Pr...   \n",
       "1  A set consists of five different odd positive ...   \n",
       "2  Given real numbers \\( a, b, c \\) and a positiv...   \n",
       "3  In triangle $ABC$, $CA = CB$, and $D$ is the m...   \n",
       "4  Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r...   \n",
       "\n",
       "                                           reasoning  \\\n",
       "0  Okay, so I need to prove this inequality: \\(\\f...   \n",
       "1  Okay, so I need to figure out how many differe...   \n",
       "2  Okay, let's try to tackle this problem step by...   \n",
       "3  Okay, so I have this geometry problem here. Le...   \n",
       "4  Okay, so I need to figure out which of the giv...   \n",
       "\n",
       "                                   deepseek_solution  \\\n",
       "0  To prove the inequality \\n\\n\\[\\n\\frac{1}{a(1+b...   \n",
       "1  To determine the number of different sets of f...   \n",
       "2  Given real numbers \\(a, b, c\\) and a positive ...   \n",
       "3  In triangle \\(ABC\\), \\(CA = CB\\), making it is...   \n",
       "4  To determine which of the given statements is ...   \n",
       "\n",
       "                               ground_truth_solution  correct  \\\n",
       "0  1. Consider the given inequality:\\n\\n\\[\\n\\frac...     True   \n",
       "1  \\n1. **Observe the Structure of \\( N \\)**:\\n  ...    False   \n",
       "2  \\nWe begin by analyzing the function \\( f(x) =...     True   \n",
       "3  1. **Identify Key Elements**: Consider \\( \\tri...     True   \n",
       "4  Given the values:\\n\\[ p = 2^{3009}, \\quad q = ...     True   \n",
       "\n",
       "                                     judge_reasoning  \\\n",
       "0  The provided solution correctly demonstrates t...   \n",
       "1  The provided solution computes a total of 25 s...   \n",
       "2  Both the provided solution and the ground trut...   \n",
       "3  The provided solution correctly follows the lo...   \n",
       "4  The solution provided correctly follows the st...   \n",
       "\n",
       "                                    extracted_answer  \\\n",
       "0  ['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...   \n",
       "1                                       ['25', '25']   \n",
       "2         ['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']   \n",
       "3                       ['D', 'DE \\\\cdot DF = DA^2']   \n",
       "4                                         ['D', 'D']   \n",
       "\n",
       "                                      extracted_gold  verifier_label error  \n",
       "0  ['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...            True        \n",
       "1                                       ['24', '24']           False        \n",
       "2         ['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']            True        \n",
       "3                       ['D', 'DE \\\\cdot DF = DA^2']            True        \n",
       "4                                         ['D', 'D']            True        "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from datasets import load_dataset\n",
    "\n",
    "# Load dataset directly from Hugging Face\n",
    "math_verify_stratos = load_dataset(\"mlfoundations-dev/math_stratos_scale_verified_with_hf\", split=\"train\")\n",
    "math_verify_stratos_with_difficulty = load_dataset(\"mlfoundations-dev/math_stratos_scale_judged_and_annotated_with_difficulty\", split=\"train\")\n",
    "\n",
    "# Convert to pandas DataFrame if needed\n",
    "math_verify_stratos_df = math_verify_stratos.to_pandas()\n",
    "math_verify_stratos_with_difficulty_df = math_verify_stratos_with_difficulty.to_pandas()\n",
    "math_verify_stratos_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "problem                  object\n",
       "reasoning                object\n",
       "deepseek_solution        object\n",
       "ground_truth_solution    object\n",
       "correct                    bool\n",
       "judge_reasoning          object\n",
       "extracted_answer         object\n",
       "extracted_gold           object\n",
       "verifier_label             bool\n",
       "error                    object\n",
       "dtype: object"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math_verify_stratos_df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "math_verify_stratos_with_difficulty_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>problem</th>\n",
       "      <th>reasoning</th>\n",
       "      <th>deepseek_solution</th>\n",
       "      <th>ground_truth_solution</th>\n",
       "      <th>correct</th>\n",
       "      <th>judge_reasoning</th>\n",
       "      <th>extracted_answer</th>\n",
       "      <th>extracted_gold</th>\n",
       "      <th>verifier_label</th>\n",
       "      <th>error</th>\n",
       "      <th>difficulty</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Let \\( a, b, c \\) be positive real numbers. Pr...</td>\n",
       "      <td>Okay, so I need to prove this inequality: \\(\\f...</td>\n",
       "      <td>To prove the inequality \\n\\n\\[\\n\\frac{1}{a(1+b...</td>\n",
       "      <td>1. Consider the given inequality:\\n\\n\\[\\n\\frac...</td>\n",
       "      <td>True</td>\n",
       "      <td>The provided solution correctly demonstrates t...</td>\n",
       "      <td>['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...</td>\n",
       "      <td>['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A set consists of five different odd positive ...</td>\n",
       "      <td>Okay, so I need to figure out how many differe...</td>\n",
       "      <td>To determine the number of different sets of f...</td>\n",
       "      <td>\\n1. **Observe the Structure of \\( N \\)**:\\n  ...</td>\n",
       "      <td>False</td>\n",
       "      <td>The provided solution computes a total of 25 s...</td>\n",
       "      <td>['25', '25']</td>\n",
       "      <td>['24', '24']</td>\n",
       "      <td>False</td>\n",
       "      <td></td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Given real numbers \\( a, b, c \\) and a positiv...</td>\n",
       "      <td>Okay, let's try to tackle this problem step by...</td>\n",
       "      <td>Given real numbers \\(a, b, c\\) and a positive ...</td>\n",
       "      <td>\\nWe begin by analyzing the function \\( f(x) =...</td>\n",
       "      <td>True</td>\n",
       "      <td>Both the provided solution and the ground trut...</td>\n",
       "      <td>['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']</td>\n",
       "      <td>['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>In triangle $ABC$, $CA = CB$, and $D$ is the m...</td>\n",
       "      <td>Okay, so I have this geometry problem here. Le...</td>\n",
       "      <td>In triangle \\(ABC\\), \\(CA = CB\\), making it is...</td>\n",
       "      <td>1. **Identify Key Elements**: Consider \\( \\tri...</td>\n",
       "      <td>True</td>\n",
       "      <td>The provided solution correctly follows the lo...</td>\n",
       "      <td>['D', 'DE \\\\cdot DF = DA^2']</td>\n",
       "      <td>['D', 'DE \\\\cdot DF = DA^2']</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r...</td>\n",
       "      <td>Okay, so I need to figure out which of the giv...</td>\n",
       "      <td>To determine which of the given statements is ...</td>\n",
       "      <td>Given the values:\\n\\[ p = 2^{3009}, \\quad q = ...</td>\n",
       "      <td>True</td>\n",
       "      <td>The solution provided correctly follows the st...</td>\n",
       "      <td>['D', 'D']</td>\n",
       "      <td>['D', 'D']</td>\n",
       "      <td>True</td>\n",
       "      <td></td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                             problem  \\\n",
       "0  Let \\( a, b, c \\) be positive real numbers. Pr...   \n",
       "1  A set consists of five different odd positive ...   \n",
       "2  Given real numbers \\( a, b, c \\) and a positiv...   \n",
       "3  In triangle $ABC$, $CA = CB$, and $D$ is the m...   \n",
       "4  Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r...   \n",
       "\n",
       "                                           reasoning  \\\n",
       "0  Okay, so I need to prove this inequality: \\(\\f...   \n",
       "1  Okay, so I need to figure out how many differe...   \n",
       "2  Okay, let's try to tackle this problem step by...   \n",
       "3  Okay, so I have this geometry problem here. Le...   \n",
       "4  Okay, so I need to figure out which of the giv...   \n",
       "\n",
       "                                   deepseek_solution  \\\n",
       "0  To prove the inequality \\n\\n\\[\\n\\frac{1}{a(1+b...   \n",
       "1  To determine the number of different sets of f...   \n",
       "2  Given real numbers \\(a, b, c\\) and a positive ...   \n",
       "3  In triangle \\(ABC\\), \\(CA = CB\\), making it is...   \n",
       "4  To determine which of the given statements is ...   \n",
       "\n",
       "                               ground_truth_solution  correct  \\\n",
       "0  1. Consider the given inequality:\\n\\n\\[\\n\\frac...     True   \n",
       "1  \\n1. **Observe the Structure of \\( N \\)**:\\n  ...    False   \n",
       "2  \\nWe begin by analyzing the function \\( f(x) =...     True   \n",
       "3  1. **Identify Key Elements**: Consider \\( \\tri...     True   \n",
       "4  Given the values:\\n\\[ p = 2^{3009}, \\quad q = ...     True   \n",
       "\n",
       "                                     judge_reasoning  \\\n",
       "0  The provided solution correctly demonstrates t...   \n",
       "1  The provided solution computes a total of 25 s...   \n",
       "2  Both the provided solution and the ground trut...   \n",
       "3  The provided solution correctly follows the lo...   \n",
       "4  The solution provided correctly follows the st...   \n",
       "\n",
       "                                    extracted_answer  \\\n",
       "0  ['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...   \n",
       "1                                       ['25', '25']   \n",
       "2         ['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']   \n",
       "3                       ['D', 'DE \\\\cdot DF = DA^2']   \n",
       "4                                         ['D', 'D']   \n",
       "\n",
       "                                      extracted_gold  verifier_label error  \\\n",
       "0  ['1/(c*(a + 1)) + 1/(b*(c + 1)) + 1/(a*(b + 1)...            True         \n",
       "1                                       ['24', '24']           False         \n",
       "2         ['(3*sqrt(3))/2', '\\\\frac{3\\\\sqrt{3}}{2}']            True         \n",
       "3                       ['D', 'DE \\\\cdot DF = DA^2']            True         \n",
       "4                                         ['D', 'D']            True         \n",
       "\n",
       "   difficulty  \n",
       "0           6  \n",
       "1           7  \n",
       "2           9  \n",
       "3           8  \n",
       "4           5  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math_verify_stratos_df = math_verify_stratos_df.merge(math_verify_stratos_with_difficulty_df[[\"problem\", \"difficulty\"]], on='problem', how='inner')\n",
    "math_verify_stratos_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create confusion matrix data\n",
    "conf_matrix = math_verify_stratos_df[['verifier_label', 'correct']]\n",
    "conf_matrix = pd.crosstab(conf_matrix['verifier_label'], conf_matrix['correct'])\n",
    "\n",
    "# Plot confusion matrix\n",
    "plt.figure(figsize=(8, 6))\n",
    "im = plt.imshow(conf_matrix, cmap='Blues')\n",
    "\n",
    "# Add numbers to each cell\n",
    "for i in range(len(conf_matrix.index)):\n",
    "    for j in range(len(conf_matrix.columns)):\n",
    "        text = plt.text(j, i, conf_matrix.iloc[i, j],\n",
    "                       ha=\"center\", va=\"center\")\n",
    "\n",
    "# Add labels and title\n",
    "plt.colorbar(im)\n",
    "plt.title('Confusion Matrix: Verifier Label vs Correct')\n",
    "plt.ylabel('Math-Verify Label')\n",
    "plt.xlabel('LLM-as-a-judge Label')\n",
    "\n",
    "# Set tick labels\n",
    "plt.xticks(range(len(conf_matrix.columns)), conf_matrix.columns)\n",
    "plt.yticks(range(len(conf_matrix.index)), conf_matrix.index)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "def bootstrap_rates(data, n_bootstrap=1000):\n",
    "    n_samples = len(data)\n",
    "    fpr_boots = []\n",
    "    fnr_boots = []\n",
    "    \n",
    "    for _ in range(n_bootstrap):\n",
    "        # Bootstrap sample\n",
    "        boot_idx = np.random.choice(n_samples, size=n_samples, replace=True)\n",
    "        boot_sample = data.iloc[boot_idx]\n",
    "        \n",
    "        # Calculate rates for this bootstrap sample\n",
    "        TP = sum((boot_sample['verifier_label'] == True) & (boot_sample['correct'] == True))\n",
    "        TN = sum((boot_sample['verifier_label'] == False) & (boot_sample['correct'] == False))\n",
    "        FP = sum((boot_sample['verifier_label'] == False) & (boot_sample['correct'] == True))\n",
    "        FN = sum((boot_sample['verifier_label'] == True) & (boot_sample['correct'] == False))\n",
    "        \n",
    "        fpr = FP / (FP + TN) if (FP + TN) > 0 else 0\n",
    "        fnr = FN / (FN + TP) if (FN + TP) > 0 else 0\n",
    "        \n",
    "        fpr_boots.append(fpr)\n",
    "        fnr_boots.append(fnr)\n",
    "    \n",
    "    # Calculate confidence intervals\n",
    "    fpr_ci = np.percentile(fpr_boots, [2.5, 97.5])\n",
    "    fnr_ci = np.percentile(fnr_boots, [2.5, 97.5])\n",
    "    \n",
    "    return fpr_ci, fnr_ci\n",
    "\n",
    "# Calculate rates and confidence intervals for each difficulty level\n",
    "results = []\n",
    "for diff in sorted(math_verify_stratos_df['difficulty'].unique()):\n",
    "    subset = math_verify_stratos_df[math_verify_stratos_df['difficulty'] == diff]\n",
    "    \n",
    "    # Calculate point estimates\n",
    "    TP = sum((subset['verifier_label'] == True) & (subset['correct'] == True))\n",
    "    TN = sum((subset['verifier_label'] == False) & (subset['correct'] == False))\n",
    "    FP = sum((subset['verifier_label'] == False) & (subset['correct'] == True))\n",
    "    FN = sum((subset['verifier_label'] == True) & (subset['correct'] == False))\n",
    "    \n",
    "    FPR = FP / (FP + TN) if (FP + TN) > 0 else 0\n",
    "    FNR = FN / (FN + TP) if (FN + TP) > 0 else 0\n",
    "    \n",
    "    # Calculate confidence intervals\n",
    "    fpr_ci, fnr_ci = bootstrap_rates(subset)\n",
    "    \n",
    "    results.append({\n",
    "        'difficulty': diff,\n",
    "        'FPR': FPR,\n",
    "        'FNR': FNR,\n",
    "        'FPR_low': fpr_ci[0],\n",
    "        'FPR_high': fpr_ci[1],\n",
    "        'FNR_low': fnr_ci[0],\n",
    "        'FNR_high': fnr_ci[1]\n",
    "    })\n",
    "\n",
    "# Convert to DataFrame\n",
    "results_df = pd.DataFrame(results)\n",
    "\n",
    "# Create the plot\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# Plot FPR with error bars\n",
    "plt.errorbar(results_df['difficulty'], results_df['FPR'], \n",
    "            yerr=[results_df['FPR'] - results_df['FPR_low'], \n",
    "                  results_df['FPR_high'] - results_df['FPR']],\n",
    "            fmt='bo-', label='False Positive Rate', capsize=5)\n",
    "\n",
    "# Plot FNR with error bars\n",
    "plt.errorbar(results_df['difficulty'], results_df['FNR'],\n",
    "            yerr=[results_df['FNR'] - results_df['FNR_low'],\n",
    "                  results_df['FNR_high'] - results_df['FNR']],\n",
    "            fmt='ro-', label='False Negative Rate', capsize=5)\n",
    "\n",
    "plt.xlabel('Difficulty')\n",
    "plt.ylabel('Rate')\n",
    "plt.title('False Positive and Negative Rates by Difficulty (Treating Math-Verify as Ground Truth)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Sample counts per difficulty level:\n",
      "difficulty\n",
      "1      4915\n",
      "2      8852\n",
      "3     10481\n",
      "4     12394\n",
      "5     17637\n",
      "6     21691\n",
      "7     19941\n",
      "8     23618\n",
      "9     18865\n",
      "10     1681\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Calculate counts for each difficulty level\n",
    "math_verify_stratos_df[\"verifier_label_parsed\"] = math_verify_stratos_df[\"verifier_label\"].apply(lambda x: \"Correct\" if x else \"Incorrect\")\n",
    "counts = math_verify_stratos_df.groupby('difficulty')['verifier_label_parsed'].value_counts().unstack()\n",
    "\n",
    "# Create the stacked bar plot\n",
    "ax = counts.plot(kind='bar', stacked=True, figsize=(10, 6))\n",
    "\n",
    "# Customize the plot\n",
    "plt.title('Distribution of Math-Verify Labels by Difficulty')\n",
    "plt.xlabel('Difficulty')\n",
    "plt.ylabel('Proportion')\n",
    "plt.legend(title='Verifier Label')\n",
    "\n",
    "# Add percentage labels on the bars\n",
    "for c in ax.containers:\n",
    "    ax.bar_label(c, label_type='center')\n",
    "\n",
    "# Adjust layout to prevent label cutoff\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Print the actual counts (optional)\n",
    "print(\"\\nSample counts per difficulty level:\")\n",
    "print(math_verify_stratos_df.groupby('difficulty').size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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